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Research and Development Laboratories 

of the 

Portland Cement Association 


Bulletin 59 

New Study on Reactions in 

Burning Cement 
Raw Materials 


L. A. Dahl 

January, 1956 

Authorized Reprint from Copyrighted 


Chicago, Illinois 
May, June, and July, 1955 

New Study On Reactions In 
Burning Cement Raw Materials 

By L. A. DAHL 



. . .The ternary system CaO-ALOa-SiOa involves the three principal oxide 
constituents of portland cement; The phase diagram is studied with refer- 
ence to the reactions which occur when ternary cement compositions are 
burned. Through this study some principles capable of extension to the 
commercial process of cement manufacture are demonstrated. These in- 
clude the relation of composition to the proportion of liquid formed in the 
burning operation, the technical lime limit, and the influence of changes in 
composition on retention of clinker coating in the kiln. The influence of 
the burning and cooling operations on the constitution of cement clinker 
is discussed briefly; 

TEM CaO-Al 2 3 -Si0 3 was reported 
in 1915 by Rankin and Wright 1 The 
paper was an outstanding contribution 
to the chemistry of portland cement, 
since the investigation was the first 
study of phase equilibria in the sys- 
tem involving the three major com- 
ponents of portland cement clinker. 
However, the principal interest to ce- 
ment chemists at the time was not in 
phase equilibria at clinkering tempera- 
tures, but in the fact that three com- 
pounds, tricalcium silicate, dicalcium 
silicate and tricalcium aluminate, were 
found to exist in portland cement 
clinker. The present paper is concern- 
ed with interpretation of the phase 
diagram with reference to the reac- 
tions which occur during the clinker- 
ing process. The three oxides, lime, 
alumina and silica, constitute about 
90 percent of the total composition of 
most portland cement clinkers. The 
components which make up the re- 
maining 10 percent have large effects 
upon phase relations, and so it cannot 

*Former Senior Research Mathematician, Port- 
land Cement Association Research and Devel- 
opment Laboratories, Chicago, 111. 

be expected that this study of the terna- 
ry system will yield exact quantitative 
information concerning phase relations 
in the cement system. However, some 
general principles may be learned, and 
these may be understood more readily 
in a study of a ternary system than in 
a study of a system involving a greater 
number of components, requiring the 
use of a space model. A ternary sys- 
tem of the type under consideration 
may be represented in a triangular 
phase diagram. Interpretation of the 
phase diagram requires application of 
certain properties of the triangular 
diagram. These properties must be 
discussed before we can enter into a 
discussion of the particular phase dia- 
gram under consideration. 

Properties of Triangular Diagram 

The properties of triangular dia- 
grams which are used in a phase dia- 
gram and in its interpretation are 
properties of all types of plane tri- 
angles, scalene, isosceles or equilater- 
al. 2 However, they have been fre- 
quently described as belonging unique- 
ly to equilateral triangles. In this study 


Fig. 1 : Triangular 
diagram of the hy- 
pothetical system 

it will be found convenient at times to 
connect points representing three co- 
existing phases by straight lines, and 
to treat the resulting triangle as a tri- 
angular diagram. Such triangles are 
practically always scalene. This mode 
of attack will be used repeatedly in 
the study of the system Ca0-Al 2 : ,- 
Si0 2 . It is therefore deemed advisable 
to describe the properties of the tri- 
angular diagram in such a manner as 
to avoid the implication that they are 
limited to equilateral triangles. 

The triangle ABC. Fig. 1, represents 
a ternary s\stem A-B-C. The three 
sides represent binary systems. A-B, 
B-C and A-C. Each vertex represents 
100 percent of the component indi- 
cated. The side opposite a vertex rep- 
resents zero percent of the component 
at the vertex. For example, the side 
AC represents zero percent B. The 
lines parallel to AC represent percent- 
ages of B in 10 percent intervals, from 
zero to 100 percent. The percentages 
of A and C are similarly indicated 
by the lines parallel to the sides BC 
and AB. The sum of the percentages 
at any point is 100. For example, M 
represents 50 percent A. 30 percent 
B. 20 percent C. 

Compositions in a binary system 
are estimated in a manner similar to 
that in a ternary system. For example, 
on the side AB, Fig. 1, which is a 
binary system, percentages of B are 
read from the zero point, at A, to the 
100 percent point at B. Point N, there- 
fore, represents 40 percent B. Reading 
in the opposite direction, point N con- 

tains 60 percent A, making a total of 
100 percent. 

A property of the triangular dia- 
gram which is frequently found use- 
ful is illustrated by the broken line 
AP in Fig, 1. All compositions on a 
line drawn from a vertex to the oppo- 
site side contain two of the compo- 
nents in the same relative proportions. 
For example, the percentages of B 
and C at M are 30 and 20, respectively, 
a ratio of 3 to 2. At P, the percentages 
of B and C are 60 and 40, respective- 
ly, a ratio of 3 to 2. This is the ratio 
of B to C at everv point on the line 

Subdivision of the triangular dia- 
gram by lines spaced at equal inter- 
vals, such as the 10 percent intervals 
in Fig. 1. is not actually necessary. 
The lines parallel to the sides are usu- 
ally omitted in phase diagrams. It is 
important, then, to know how to lo- 
cate the point representing any given 
composition or, conversely, to deter- 
mine from the location of any given 
point the composition it represents. 
In the case of a binary system, the 
distances from any given point to the 
ends of the line represent relative 
proportions of the components, and 
are converted to fractional weights by 
dividing each distance by the length 
of the line. It must be borne in mind 
that the distances are taken in revers 
order. For instance, the relative pro- 
portions of A and B in N are the die 
tance of N from B and A, respective!} 
In showing only a portion of a phase 
diagram it is sometimes convenient t 





Fig. 2: Estimation 

of composition at a 
given point M 

designate 10 percent intervals, or oth- 
er suitable intervals, along the sides 
of the diagram, as shown along part 
of the base AC in Fig. 1. These points 
are represented by short segments of 
the longer lines in the figure. 

Fig. 2 illustrates a method of esti- 
mating the composition at any given 
point within a triangular diagram, in 
this case point M, which is in the 
same location as in Fig. 1. Straight 
lines are drawn from M to one of 
the sides and parallel to the other two 
sides. Any side may be selected, but 
it is usually convenient to select the 
longest side, in this case the side AC. 
The lines MV and MW are parallel 
to the sides AB and BC, respectively. 
The intersections of these lines with 
AC divide the latter into three seg- 
ments, and the lengths of these seg- 
ments are relative proportions of A, 
B, and C in M. The intermediate seg- 
ment VW is the relative proportion of 
B, the component at the opposite ver- 
tex. The segment for A is the one 
farthest from A, and the one for C is 
the one farthest from C. The proced- 
ure is reversed for locating any given 
composition in the diagram. Upon di- 
viding the length of each segment by 
the length of the side AC, it is found 
that the composition of mixture M is 
50 percent A, 30 percent B, 20 per- 
cent C. 

The System CaO-ALO : ,-SiO a 

The phase diagram of the system 
CaO-Al 2 3 -Si0 2 is presented in Fig. 
3. This diagram is essentially the same 

as the original phase diagram of Ran- 
kin and Wright, 1 but with such modi- 
fications as were found necessary as 
a result of later investigations. 3 * - 5| 6 
These modifications do not affect the 
portion of the system under study 
here, and will therefore not be dis- 

The phase diagram is a graphic rep- 
resentation of the data obtained in 
the investigation of the system. It not 
only reduces a large volume of data 
to a convenient form, but it also pro- 
vides a base on which to operate in 
the interpretation of the data; that is, 
in applying the properties of the tri- 
angular diagram in the interpretation 
of the phase diagram, we are actually 
interpreting the data from which the 
phase diagram is obtained. 

Each point in the phase diagram 
represents a state of equilibrium, or a 
state of rest. Since a process repre- 
sents changes of some kind, not a 
state of rest, the phase diagram does 
not represent processes. It is useful, 
however, in studying processes, with 
the aid of additional information or 
assumptions. For example, the normal 
course of crystallization of a liquid in 
the system may be traced by assuming 
that at each temperature a state of 
equilibrium is attained before cooling 
to a slightly lower temperature. Each 
successive equilibrium state may be 
found from the phase diagram. The 
course of crystallization in an ac- 
tual process may differ considerably 
from this if the assumption of con- 
tinuous attainment of equilibrium does 
not apply to the process. 





Fig. 3 : Phase dia- 
gram of the system 

CaO-AU0 3 -Si0 2 

Rankin and 
Wright, as modi- 
fied by later in- 

When a pure crystalline compound 
is heated, it may decompose, or it 
may arrive at a definite temperature, 
or melting point, without decomposi- 
tion. In the latter case it melts, with- 
out change of temperature, until it is 
complete!} transformed into a liquid 
of the same composition. Upon cool- 
ing, the liquid solidifies at the same 
temperature; that is. at the melting 
temperature. In a mixture such as 
th- ncountered in the system CaO- 
AJ*0 3 -Si0 2 the situation is quite dif- 
ferent. The mixture starts to melt at 
some definite temperature, and some 
rystalline phases are present as that 
temperature is maintained. The quanti- 
ty ol liquid increases as the tempera- 
ture rise Eventually a temperature 
is reached at which all of the crystal- 


line substances are absent. This is 
sometimes termed the melting point. 
However, it is not a melting point in 
the vime sense as in the case of the 
pure cnstalline compound which melts 
without decomposition. The solid 
phase present at a temperature slightly 
below the complete fusion is not of the 
ame composition as the liquid, but can 
exist in equilibrium with the liquid 
until the temperature is raised to com- 
plete the process of fusion. Because 
of this difference between the melting 

point of a cnstalline compound and 
the temperature at which a mixture 
becomes completely liquid, we prefer 
to term the latter the "temperature of 
complete fusion." 

The significance of the various 
points, curves, and areas in the dia- 
gram may be understood by consider- 
ing one of the methods of locating 
them. Let us suppose that we are 
starting out with no knowledge of 
phase relations in the s; em CaO- 
Al a 3 -SiO a . which we propose to in- 
vestigate. All that we have at the out- 
set is the triangle, with CaO, A1 2 ;1 . 
and SiO a designated at the vertices. 
Mixtures represented by points in the 
diagram are heated until completely 
liquified. Upon cooling, crystalline 
phases separate out. Usually only on 
crystalline phase separates out at first, 
and this is followed by the appearance 
of others as crystallization proceeds. 
The first one to appear is known as 
the priman phase. A particular crys- 
talline phase may be the priman 
phase for liquids in one region of the 
diagram, while another crystalline 
phase may be characteristic of another 
region. The problem is to map out 
these "priman phase regionv A large 
number of compositions must be in- 
vestigated to establish the boundarie 


between the primary phase regions. 
In each region the primary phase must 
be identified. A common method is 
to heat each mixture until it is com- 
pletely melted, then cool to a temper- 
ature slightly below the temperature 
of complete fusion. The mixture is 
then "quenched" — that is, cooled so 
suddenly that further crystallization 
does not occur. The mixture then con- 
sists of glass, in which the primary 
phase crystals are imbedded. The 
identity of the crystalline phase is de- 
termined by its optical properties, as 
observed microscopically. 

In the course of locating boundaries 
between primary phase regions and 
identifying the primary phase in each, 
the temperature of complete fusion of 
each mixture is observed and record- 
ed. At this stage the boundaries of 
the primary phase regions have been 
drawn in the diagram, the primary 
phase in each region has been indi- 
cated, and the observed temperatures 
have been used to locate isotherms, 
as in Fig. 3.* All of the experimental 
data are now shown in the diagram, 
but there are some further steps in- 
volved in completing Fig. 3, for con- 
venience in the interpretation of the 
diagram. The composition of each 
crystalline phase is calculated from 
its chemical formula, and a point 
representing that composition is lo- 
cated in the diagram. For example. 
3CaO*Al 2 0». or tricalcium aluminate, 
is one of the primary phases. Its com- 
position is 62.26 percent CaO, 37.74 
percent A1 2 ; „ and it is located on the 
base at a point such that its distance 
from the CaO vertex is 0.3774 times 
the length of the base. Points repre- 
senting the other primary phases are 
located in a similar manner. 

Another addition to the diagram is 
the system of dotted lines separating 
the diagram into smaller triangles rep- 
resenting final products of crystalliza- 
tion. In the case of each triangle the 
crystalline phases at its vertices are 
the crystalline phases present in all 
compositions within the triangle when 

*A11 temperatures in this paper, both in fig- 
ures and text, are expressed in degrees Cent 

crystallization is completed in a slow- 
cooling operation. A definite plan is 
followed in determining which points 
representing primary phases should be 
connected by straight lines. If two 
primary phase regions are adjacent, a 
line is drawn between the points rep- 
resenting those phases. For example, 
the primary phase regions for CaO- 
•Al,(V2Si6 and AI 2 3 adjoin. A line 
is therefore drawn between the points 
representing those phases. 

The interpretation of the phase dia- 
gram is simplified by the assumption 
that the crystalline phases are pure 
compounds. According to Rankin and 
Wright, 1 solid solution "occurs only 
in the case of CaOSi0 2 and then only 
to the extent of 2 percent with each 
of the compounds with which it is 
associated; namely, SiO,., 3Ca02Si0 2 , 
CaOAl 2 3 '2Si0 2 , and 2CaOAl 2 3 - 
•Si0 2 ." This does not involve the por- 
tion of the system in which we are 
interested. However, the fact that the 
boundary between the aC 2 S region 
and one of the /3C S S regions in Fig. 3 
is clearly not an isotherm indicates that 
solid solution in the C 2 S phase influ- 
ences the a-/3 inversion temperature. 
This is also shown in Rankin and 
Wright's Table VI. The assumption 
that the crystalline phases are pure 
compounds is not strictly correct. 
However, the extent of impurity in 
the crystalline phases in the ternary 
system is not sufficient to necessitate 
taking it into account in the interpre- 
tation of the ternary phase diagram 
with reference to the manufacture of 
Portland cement clinker. We shall, 
therefore, continue to treat the crys- 
talline phases as pure compounds. 

In describing a procedure by which 
the various regions in Fig. 3 may be 
mapped out, we emphasized that all 
liquids in any particular region are 
alike with reference to the first crys- 
talline phase which appears upon cool- 
ing. That emphasis was necessary be- 
cause we were describing a procedure 
in which the essential operation is de- 
termination of the first, or primary, 
phase. However, interpretation of the 
phase diagram involves a more precise 
concept of the significance of the re- 



Fig. 4: The system 

CaO-C 8 S-C ls A s , 

shown below. 



gions then boundaries and intersec- 
tions of the boundary curves. To illus- 
trate. let us consider the CaO priman. 
phase region in Fig. 4,* which is a 
portion of the phase diagram in Fig. 
3. Liquid R on the 1700 deg. isotherm 
can exist by itself as a liquid at that 
temperature, or it ma\ exist at equi- 
librium with am quantity of crystal- 
line CaO at that temperature. That is. 
a mixture ol liquid R and solid CaO 
max be maintained at that tempera- 
ture indetinitclv without the occur- 

rence o\ any reaction. All mixtures of 
liquid R and solid CaO are on the 
dotted line CaO-R. Therefore, all mix- 
tures on that line between CaO and R 
are composed of solid CaO and liquid 
R when equilibrium is attained at 
1700 dee. 

In Fitf. 4 abbreviated formulas are u f< 

mpounds of CaO, AhO and SiO-. These ox- 
ides are designated as C, A r and S, respective- 
ly. Thus, CaS = 2CaO*SK>2 ; CaS = 3CaO«SiOi ; 

\ = SCaO'AleOa ; and Ci>At = 12CaO*7Al 
Os. These abbreviated formulas will be used in 

1 he remainder of the paper. 

Part II: The course of crystallization 



CRYSTALLIZATIONl of a liquid in the 

system mav be traced, let us consider 
liquid X. which is on the line CaO-R. 
Judging from the position of X with 
reference to the isotherms and the 
melting point of CaO (2570 deg.), we 
would estimate the temperature of 
complete fusion of X to be about 2350 
deg.. and will assume that to be the 
ise. Solid CaO appears when liquid 
X is cooled just below 2350 deg., and 

•i"The normal con of cr tllization refers to 

n n ideal process, in which equilibrium is at* 
taintd at each temperature before another 
small decrease in temperatui 

increases in amount as the tempera- 
ture is lowered. As the quantity of 
solid CaO increases the liquid changes 
in composition in a direction away 
from the CaO vertex. At 1700 deg, 
the liquid is at point R. Since the line 
CaO-X is one-fourth of the line CaO- 
R. the mixture consists of 25 percent 
liquid R and 75 percent solid CaO 
at 1 700 deg. 

As the mixture cools below 170 
deg. the liquid continues to change in 
composition in a direction directly 
away from CaO until at about 1550 
deg. it arrives at T. which is on the 
boundan between the CaO and C : ,S 


primary phase regions. It might seem 
that with a little further cooling the 
liquid would change in the same di- 
rection to a point inside the C 3 S re- 
gion, such as T x . However, the only 
solid phase with which a liquid in the 
C 3 S region can exist in equilibrium is 
C3S. Movement of the liquid to Ti 
would involve a decided change from a 
state in which the phases are solid CaO 
and liquid to one in which they are solid 
C 3 S and liquid. The matter may be 
tested by drawing the line C 3 S-T X . 
Since X is not on the line CaS-T^ this 
is an impossible condition if equi- 
librium is to be continuously attained. 
On the other hand, the liquid might 
change in composition along the curve 
TD, and this possibility can be tested. 
Since V is on the boundary between 
the CaO and C 3 S primary phase re- 
gions, and also on the 1500 deg. iso- 
therm, liquid V may exist in equilibri- 
um with CaO and C 3 S at that tempera- 
ture. Without drawing the necessary 
lines, it is readily seen that X is in 
the triangle C 3 S-V-CaO. It is there- 
fore known that the liquid follows 
the curve TV and, by the same pro- 
cedure, that it follows the curve be- 
yond V to D. 

The primary phase regions for CaO, 
C 3 S and C : ,A meet at point D. At 1470 
deg., liquid D is capable of existing 
in equilibrium with these three solid 
phases. CaO and C 3 S are the solid 
phases present when the liquid arrives 
at D, but C 3 A appears and crystalliza- 
tion proceeds with liquid D present, 
so that there are now four phases 
present, liquid D and solid CaO, C 3 S 
and C,A. The process continues with- 
out change of temperature until one 
of these phases disappears. There are 
four combinations of three phases 
each, as follows: 



CaO, C 3 S, liquid D 
CaO, C3A, liquid D 
C 3 S, C 3 A, liquid D 

The first combination represents the 
phases present when the liquid arrived 
at D, Mixture X cannot be formed 
from the phases in combinations 2 

and 3, since X is not in the triangle 
formed by joining the points indicated 
in either combination. Combination 4 
is possible, since X is in the triangle 
CaO-C 3 S-C 3 A. In this way it is found 
that crystallization of mixture X pro- 
ceeds to completion with the liquid 
path ending at D. A study of the 
course of crystallization of other mix- 
tures in triangle CaO-C 3 S-CaA leads 
to division of the triangle into three 
areas which differ in the order of ap- 
pearance and disappearance of solid 
phases in the normal course of crys- 
tallization. In each area, normal crys- 
tallization begins with the appearance 
of the primary phase, CaO, and ends 
with liquid D present until the last 
drop of liquid disappears. The three 
areas, with the solid phases listed in 
the order in which they are present, 
are indicated below. 

1. Triangle CaO-C 3 S-k. 

CaO; CaO, C,S; CaO, C 3 S, C 2 S 
(at point K); CaO, C 3 S; CaO, 

v^ 3 o, L'jA. 

2. Triangle CaO-k-d. 

CaO; CaO, C 3 S; CaO, C 3 S, C 3 A. 

3. Triangle CaO~d-C 3 A. 

CaO; CaO, C 3 A; CaO, C 3 S, C 3 A. 

The reason for the plan which was 
followed in choosing the pairs of com- 
pounds which are joined by the dotted 
lines in Fig. 3, may now be under- 
stood. For each triangle so obtained 
there is a corresponding point at which 
three primary phase regions meet, and 
these primary phases are those at the 
vertices of the triangle. At this point 
crystallization of all compositions in 
the triangle are completed. For exam- 
ple, liquids in the triangle C 3 S-C 2 S-C 3 A 
normally complete their crystallization 
with the liquid at point E, Fig. 4, until 
the last drop of liquid disappears, 
leaving only solid C 3 S, C 2 S and C 3 A. 
Point E is outside of the triangle 
CtS-CoS-CA, and is therefore classed 
as a peritectic point. Point D is also 
a peritectic point. A point inside the 
triangle which defines the range of 
compositions that complete their crys- 
tallization at the point is classed as a 


eutectic point. Both eutectic and peri- 

tectic points, are invariant points. 

When the liquid phase is at an in- 
variant point, changes in proportion 
ol phases occur without change in 
temperature. This was shown in the 
rystallization ol composition X. Fig 

4. Wh the liquid arrived at D, three 
phase were present, solid CaO. C«S, 

nd liquid D. Another phase, solid 

C \ appeared, and there were then 

f< r pi pri . nt. 1 he proportions 

I t he phages changed until li 11) 

o phase liquid 1). disapp* red. 
! I ian n propoi tions ol phase 

u i .i constant temp ature 

chan£ Ik intent. Dui 

tllizal vei sc pi OC 

i >n, .it .hi invaj m i int 

.i tei maintai i- 

at until the s in 

m; pleted. 1 his 

the ci ined when 

m h tin 
\\ hen 1 1 dil 
he d mini- 

I pai ilai 

there be 


I V 

J v 





it Is 

ur an r 

1 1 
I Ik a i 





f - 

I his ii .d 

it [ Is 

The System C S-C S C A 

. i ' 1 








ised i i 



to I 

) S 


n th< 
( ,A * | I • 

• ! is 



«. * 

Invariant points in the system CaO 
C*S-CuA« are listed below : 





aO i 
• 7.5 

A IsOs 


M 2065 




B 15 

t 0, 




G 1 5 

I A 





K 1 


c C*S 




L J 






H 1385 


, ( 

11 2 


D 14 


1 \ 


K 1 : 

( - 




1 he final products of crystallization 
t liquids or partial!) fused n terials 
in the triangle ( ,s ( $ i \ an the 
compounds at the veil es ot the tri- 
angle. In studying the el which 
occur in the clinkering pn it is 
convenient to transform ovule m- 
posi tions to composition expressed in 
tenni >i these compounds. I he com- 
pound compositions may be (ciliat- 
ed for mixtures oi the thn iid< 

■ Inch have not acti >lv been com- 

hn i to foi ra the comp mds. I h 
Iculated compound composite m.o 
be ti l the potential compositioi 
to avoid the implication thai th< com- 
pounds an nee sarih pi rM in th 

leu d | tions In an) ease 

howevei . the potent omj sition u = 

dieates the ( I the I m- 

pou Ineh WOUld l v pr( nl if ll> 

oxides were eoi to l< i 1 

(hi unids. I Ik i ilia! m- 

posiiuMi ma) be dated from i 

le v. position I sul ituti i in 

ihe follow i quali in \s bich th 

eienl I up 19 . ati 

ic v ighth 

4 i 

< i 

( i 



Ii these cqu ihi chemical !<•: 

ml I he in- 

let ui >xid<; 5 I * »i c x 

lion ^ \ 1 i 

I ,A 0J i.A 


ul\ I - A I he tri- 

al doe' 

I he poti iiij 

turet in : i s( i A ai 

i grapi i 

( ( ,A r divj d ii 1 

p f the com- 

s d J jn 

i 1 . 

I ( .S ( 

the U 

s line a 


SUfflCR ' 


Fig. 5 : Final prod- 
ucts of crystalliza- 
tion in the system 

C S-C,S-C,A 

CaO to convert all of the Si0 2 present 
to CaS and all of the ALG* present to 
C ;l A. Any excess of CaO beyond that 
amount of CaO must be un combined. 
This is in addition to any tree lime 
which may be present bee, i use of poor 
burning or other reasons. The line 
representing the theoretical lime limit 
also represents zero percent potential 
GsS. Thus, the theoretical lime limit 
is attained when the potential C,S is 
zero, or when 

CaO=2.80 SiOa f-1.65 Af 0a. 

Point X on the line C S — C : ,A rep- 
resents the composition 41.9 percent 
C 2 S, 58.1 percent C :l A. That is the 
composition when crystalline equilib- 
rium is attained at 1455 deg, It will be 
shown presently that this mixture has 
a quite different phase composition 
when the heat content is maximum at 
that temperature. 

When a mixture in the system 
CaS-CaS-CaA is maintained at 1455 
deg., liquid E and the solid phases 
CaS, CaS and C,A may coexist in a 
state of equilibrium. However, as heat 
is added to the system at 1455 deg., 
the maximum heat content and maxi- 
mum quantity of liquid E are attained 
simultaneously, and one of the solid 
phases disappears. The proportions of 
solid phases and liquid may be esti- 
mated by joining point E, Fig- 4, 
with the points representing the solid 

phases. I his is shown in 6 tor the 

case in which solid ( t \ disappears. 

leaving C f S, C S and liquid I I he 

u.nglcs C,S-( ,S-C,\ and C St vE 

have a common b and the lim 

representing potential ( ; \ in one an 

per cent liquid in the other, arc con- 
sequent!) parallel. It is apparent that 

for cement compositions m the tri- 
angle C,s-C,S-\ the percent liquid E 
proportional to the potential ( f A. 

Considering the position ol point X 
on the line ( ,S-I '.. and the lengths of 

the segments ( ,s-\ and \E, it is seen 
that ; 1455 deg maximum heat con- 
tent, a mixture oi that composition is 

composed of $3.5 percent ( ,S, • 5 
percent liquid E. It the mixture is 
quenched while in that state, so that 

the liquid is frozen to a glass, the 
cooled material will ntain $3 5 per- 
cent C Si 66.5 percent glass On the 
other hand, if it is cooled slowly, so 
that normal crystallization occurs, it 
will contain 41.9 percent C*S, 58.1 
percent C t A. and no CaS- As men- 
tioned previously in discussing Fig. 5, 

the appearance of C,S in greater quan- 
tity than in the crystallized product ap- 
plies to all compositions in the system 
C ,S-C \S-C,A, but the effect is greatest 

at point X. It is due to the fact that in- 
variant point E is outside of the svs- 
tem, in a direction away from the 
C 3 S vertex. If point E were inside the 


Fig. 6 : Percent liq- 
uid at 1455 deg. 

'max, heot con- 
tent* for composi- 
tions in the trian- 
gle C..S-C_.S-x 

triangle C : ,S-C 2 S-C f A. this effect would 
not appear. The increase in the per- 
centage of C ;1 S through quenching at 
the temperature of liquid formation 
may seem to offer promise as a meth- 
od of manufacturing a high early 
strength cement (high C :f S ) . However, 
the condition applies to portland ce- 
ments made from the three oxides. 
and does not apply when other oxides, 
Mich as Fe 2 3 , or Fe 2 :4 and MgO, 
are added to the system. It serves to 


illustrate the fact that burning and 
cooling conditions play an important 
part in determining the chemical na- 
ture of the final product. 

In Fig. 7 the proportions of liquid 
at 1455 deg., maximum heat content, 
are shown for the entire system C 3 S- 
C\S-C 3 A. In the discussion of Fig. 6 
it was shown that, for compositions in 
the triangle C 3 S-C 2 S-X, solid C 3 A dis- 
appears when the quantity of liquid 
reaches a maximum at 1455 deg., and 
the percent of liquid is proportional 
to the potential C»A. A similar situa- 
tion exists in the triangle C^S-X-dA. 
Here C-S disappears when the quan- 
tity of liquid reaches a maximum at 
1455 deg., and the percent of liquid 
is proportional to the potential C 2 S. 
That the latter is true may be readily 

Fig. 7 : Percent liq- 
uid at 1455 deg. 

max. heat con- 




seen. Lines representing 10 percent 
intervals of potential C 2 S are paral- 
lel to the QsS-CsA side of the tri- 
angle, as shown in Fig. 5. The lines 
representing 10 percent intervals of 
liquid in the triangle C 3 S-X-C 3 A are 
also parallel to that side, so that the 
percent of liquid is proportional to 
the potential C.S. 

The percent of liquid in a mixture 
in the system C 3 S-C 2 S-C 3 A, at maxi- 
mum heat content at 1455 deg., may 
be estimated from Fig. 7 by locating 
the composition in the diagram. The 
quantity of liquid may be increased 
by raising the temperature. This will 
be considered presently. However, it 
is of interest to consider the relation of 
composition to liquid content at 1455 
deg. (the lowest clinkering tempera- 
ture) in a manner more closely re- 
lated to control of composition in the 
manufacturing process. The raw mate- 
rials commonly used in the manufac- 
ture of portland cement clinker are 
limestone and clay or shale. For a 
comparable situation in the ternary 
system, we will let pure CaO represent 
limestone and a mixture composed of 
77 percent Si0 2 , 23 percent ALO rJ rep- 
resent clay. The line CaO-B in Fig. 7, 
when extended, passes to the point 
representing the clay. These materials 
will be referred to as limestone and 
clay, to carry out the comparison with 
the commercial process. It will be as- 
sumed that the materials are pulver- 
ized. Proportions of the two materials 
will be expressed on an ignited weight 

Starting at 55 percent limestone and 
passing toward the CaO vertex, the 
C3S-C2S-C3A triangle is encountered 
at point C (64.5 percent limestone). 
At this point, 25 percent liquid E is 
present at maximum heat content, 
sufficient to cause the agglomeration 
of particles into a clinker. As the per- 
cent of limestone is increased, the pro- 
portion of liquid is reduced, until at 
F, (70.5 percent limestone) about 20 
percent liquid E is present. Through- 
out this range, the quantity of liquid 
is sufficient to act as a medium through 
which chemical reaction can occur 

toward the attainment of equilibrium; 
that is, the temperature of liquid for- 
mation, 1455 deg., is sufficient for the 
accomplishment of the desired reac- 
tions, and there is no need of raising 
the temperature. 

In the region between C and F the 
effect of changes in percentage of 
limestone on liquid content is not 
great, since the lines representing 10 
percent intervals in liquid content are 
far apart, and the line CaO-B makes 
only a small angle with them. After 
passing the line CS-E at F, the per- 
cent of liquid is governed by the po- 
tential C 2 S, as shown previously. In 
this region the lines representing 10 
percent intervals of liquid E are close- 
ly spaced, and they are crossed almost 
at right angles by the line CaO-B. The 
small increase of 1.2 percent in the 
proportion of limestone in passing 
from F to G is accompanied by a de- 
crease in liquid content from about 
20 percent to zero. Higher tempera- 
tures are required to secure sufficient 
liquid, but in this range of composi- 
tions the increase in liquid content 
may be accompanied by other un- 
desirable conditions which will be dis- 
cussed presently. 

One of the most important consid- 
erations is controlling proportions of 
materials in the manufacture of ce- 
ment clinker is that of securing a 
liquid content which will lead to the 
attainment of equilibrium in a reason- 
able time. From the foregoing study 
of Fig. 7 with reference to conditions 
at the temperature of liquid forma- 
tion, it may be readily understood that 
for ternary compositions between C 
and F the control of proportions of 
limestone and clav is not nearlv as 


critical as in compositions between F 
and G. In fact, the effect of a change 
of 1.00 percent in the percentage of 
limestone on the percent of liquid E 
is 24 times as great between F and G 
as it is between C and F. 

It has been found in the foregoing 
study that in the case of mixtures in 
the triangle C3S-X-CS, the quantity 
of liquid at 1455 deg. is proportional 


to the potential C 3 A, while in the tri- 
angle CaS-X-C^A the quantity of 
liquid E is proportional to the poten- 
tial C a S. This has been demonstrated 
graphically. A similar situation exists 
when other components are added to 
the system, as in the case of commer- 


cial portland cement clinker. To dem- 
onstrate this similarity it will be nee- 

essary to compute percentages of solid 
phases and liquids, since graphic meth- 
ods such as those which have been 
used for the ternary system are not 
adequate when the number of com- 
ponents is increased. The method of 
computing phase composition, that is, 
composition expressed in terms of the 
phases present, will now be described. 

Part III: Computation of phase composition 


■■■ computation of phase composition, 
let us consider the problem of calcu- 
lating the weight fraction of liquid E 
in a mixture of the composition 70/15 
percent CaO. 830 percent A1 2 3 . 
11.55 percent Si0 2 . Liquid E, which 
capable of existing in equilibrium 
with solid C 3 S. CzS and C3A at 1455 
deg. 3 has the composition 58.3 percent 
CaO. 33.0 percent A1 2 3 . 8.7 percent 
Si0 2 . As this liquid is formed it with- 
draws CaO. Al 2 O a and S1O0 from the 
solid portion of the mixture in the 
proportions required for its formation, 
as indicated in the composition of the 
liquid. Let m represent the weight 
traction of liquid at any given time. 
Then in 100 grams of mixture, the 
components in the solid residue are 
as follows: 


CaO -- 

= 70.15-58.3m 



Al O = 

= 8.30-33.0*1 



SiO = 

- 21.55- 8.7m 


For anv \alue of m % from zero to a 
certain maximum, the equations will 
give the percentages of CaO, AI.O3 
and S1O2 in the solid residue, ex- 
pressed in terms of the mixture as a 

hole. The maximum value of m re- 
mains to be determined. It is apparent 
that m cannot exceed 8.30/33.0, or 
2515, since the Al 2 :i in the residue 
is then zero, and no Al 2 O a remains for 

ontinuing the formation of liquid. 
However, this method of determining 
the maximum value of m assumes 
that any residue which remains is 
capable of existing in equilibrium with 
liquid E. This assumption is not 
sound. The residue must consist onlv 
of solid phases capable of existing in 

equilibrium with liquid E; that is, one 
or more of the phases C 3 S, C 2 S and 
C3A. To obtain a value of m which 
will leave such a residue, the composi- 
tions of both liquid E and the mixture 
may be expressed in terms of C 3 S, C 2 S 
and C3A. The potential compound 
composition of each may be computed 
by substitution in equations 1-3, ob- 
taining the compositions indicated be- 


Liquid E 


66. 1 % 


C 2 S 









The potential C :J S in liquid E is nega- 
tive because liquid E is outside of tri- 
angle C3S-C2S-C3A in a direction away 
from the C.<S vertex, as shown in Fig. 
4, The potential compositions are used 
in setting up equations similar to 
equations 4-6. as follows: 

Solid C 3 S =66.1 
Solid C,»S = 11 .9 
Solid C :J A = 22.0 






The value of m is the smallest value 
which will reduce one of the equa- 
tions to zero. From equation 8. 
777=11.9/63.0. or 0.1889. From equa- 
tion 9. 777 = 22.0/87.4, or 0.2517. The 
smaller of these values. 0.1889, is the 
maximum value of m to be applied in 
equations 4-6 or 7-9. Substituting in 
equations 7-9. we obtain the follow- 


Solid CaS = 



0.1889 = 

Solid OjS = 



0.1889 = 


Solid CaA — 





Lie 1 E = 





The percentages of phases obtained 
by the foregoing method is in har- 
mony with the required conditions, 
that the amount of liquid attains a 
maximum through the disappear- 
ance of one of the solid phases, and 
that the residue is composed of phases 
capable of existing in equilibrium with 
the liquid. 

Comparison with the Quaternary 
System CaO-AI 2 3 -Si0 2 -Fe 2 3 

The quaternary system CaO-AI 2 3 - 
Si0 2 -Fe 2 3 has been investigated with 
reference to portland cement technol- 
ogy by Lea and Parker 7,8 and by 
Swayze. Lea and Parker investigated 

be used to avoid such difficulties. The 
system within the quaternary system 
which corresponds to the system 
C 3 S-C 2 S-C 3 A in the ternary system is 
the system C^S-CaS-CaA-C^R Port- 
land cement clinker may be made 
from mixtures in either system, but 
those in the quaternary system may 
be burned at a lower temperature, and 
resemble commercial clinker more 
closely because of the presence of 
Fe 2 3 , which is a constituent of all 
commercial cements. The potential 
composition of mixtures in the system 
CaS-CsS-CiA-CiAF may be calculated 
by substitution in the following equa- 

C,S = 


c 2 s= 

C 3 A = 
C 4 AF 

4.0715 CaO-7.5996 SiO,- 1.4297 Fe a O :l -6.7182 A1 2 3 
8.5996 SiOs+1.0786 Fe 2 O 3 +5.0682 Al 2 O 3 -3.0715 CaO 

2.8665 SiCVO.7544 C 3 S 
= 2.6501 Al 2 3 -1.6919 Fe 2 3 
= 3.0431 Fe 2 3 


I 11a) 


the system CaO-C 2 S-C 5 A 3 -C 4 AF. The 
compound 4CaOAl 2 3 *Fe 2 3 , desig- 
nated here as C 4 AF, had been report- 
ed earlier by Hansen, Brownmiller 
and Bogue 10 as the ferric oxide com- 
pound in portland cement, and was 
therefore selected as one of the com- 
ponents of the system to be investi- 
gated. In his investigation of the ter- 
nary system CaO-C 5 A 3 -C 2 F, Swayze 
discovered the existence of a com- 
plete series of solid solutions from 
C 2 F to a new compound, CoA 2 F. The 
composition C 4 AF is in this series. In 
order to include the entire solid solu- 
tion series in the quaternary system 
under investigation, it was necessary 
to investigate the system CaO-C 2 S- 
C 5 A. r C 2 F, which includes a wider 
range than the system investigated by 
Lea and Parker. Since some of the 
data required for mathematical treat- 
ment are lacking in Swayze's investi- 
gation, we will base our studies here 
on Lea and Parker's data. 

A space model in the form of a 
tetrahedron is required for representa- 
tion of a quaternary system. It will 
not introduce complexities in this 
study, since the method of computa- 
tion which has been described will 

With the exception of terms involving 
Fe 2 : „ equations 10-12 are identical 
with equations 1-3. 

The point in Lea and Parker's qua- 
ternary system corresponding to point 
E, Fig. 4, in the ternary system is des- 
ignated as invariant point T 2 . The 
liquid at this point is capable of exist- 
ing in equilibrium with solid C 3 S, C 2 S, 
C^A and dAF at 1338 deg. The oxide 
composition and the potential com- 
pound composition of liquid T 2 are 
given below, the latter computed 
substitution in equations 10-13. 

Composition of liquid T 2 
Oxides Compounds 


SiO a 




A1 2 3 


C 2 S 


Fe a 3 



D /S~*Jm0 





In the ternary system we found that 
the potential C 3 S at point E is nega- 
tive, indicating that the point is out- 
side of the triangle C 3 S-C 2 S-C 3 A in a 
direction away from the C 3 S vertex. 
It was this condition that led to the 
presence of larger quantities of solid 
C 3 S when liquid E is present than 
when crystallization is complete. The 
situation is not the same in the qua- 


ternary system. At point T 2 the poten- 
tial percentages of the compounds are 
all positive. The potential C 3 S is a 
small positive value, indicating that 
point T 2 is barely inside the tetrahe- 
dron C3S-G.S-C3A-C4AF. Lea and 

Parker express some doubt as to 
whether the point is inside the tetra- 
hedron (a eutectic) or outside (a peri- 
tectic), since small changes in the 
composition of the point, within the 
experimental error of determination, 
could place it on either side of the 
face of the tetrahedron. For our pur- 
pose it will be assumed that the re- 
ported composition is not subject to 
any error of this kind. 

As an example of the computation 
of phase composition, we will consider 
the problem of calculating the per- 
centages of solid phases and liquid T 2 
in a mixture having the potential com- 
position 44.8 percent C,S, 35.6 per- 
cent C,.S, 7.0 percent C.*A, 12.6 per- 
cent C 4 AF. Equations for the percent- 
ages of solid phases may be set up in 
the same manner as equations 7-9, 
with m representing the weight frac- 
tion of liquid T 2 . as follows: 

Solid C :j S - 

: 44.8 - 

- 1.4m 


Solid C,.S = 

= 35.6- 

- 16.2m 


Solid C.,A = 

: 7.0 - 

- 32.2m 


Solid C,AF = 

: 12.6 - 

- 50.2m 


Equating each of the right-hand mem- 
bers to zero, and solving for m 9 it is 
found that equation 16 gives the low- 
est value of m 3 that is, 7.0/32.2, or 
0.217. Substituting in the equations, 
we find that 

Solid C :J S : 

= 44.5% 

Solid C 2 S : 

= 32.1 

Solid C 3 A : 

= 0.0 

Solid C*AF : 

= 1.7 

Liquid T 2 : 

= 21.7 


Equations 14-17 refer to one par- 
ticular mixture in the system, for 
which the C^A equation gave the low- 
est value of m 9 indicating that the 
potential C 3 A determines the percent 
of liquid T 2 . In view of the complete 
range of compositions of mixtures in 
the system it may be readily under- 

stood that in one range of compo- 
tions the potential C-jA determines the 
percent of liquid, in another the po- 
tential C 2 S is the governing factor, 
etc. The four regions correspond to 
the areas C 3 S-C 2 S-X and C3S-C3A-X, 
Fig. 7, in which the percent liquid is 
determined by the potential C3A or 
C 2 S, respectively. In the space model 
of the quaternary system these regions 
are separated by planes meeting at the 
point T 2 . 

In the cement industry the com- 
pounds C 3 A and C4AF are frequently 
referred to as "fluxes." The A1 2 3 and 
Fe 2 8 which enter into the formation 
of these compounds are present in the 
raw materials from which portland ce- 
ment clinker is made, and are not 
commonly added to the raw mix to 
serve as fluxes. However, since they 
play a part in promoting fusion, they 
may be regarded as fluxes to the ex- 
tent that they serve that purpose. 
Since it has been found that the per- 
cent of liquid is governed by the po- 
tential percentage of the compound 
which disappears when the liquid is 
formed, it is preferable to refer to the 
compounds, rather than the oxides, as 
fluxes. When the potential percentage 
of a particular compound determines 
the percent of liquid, the compound 
may be regarded as a flux, since it 
promotes fusion. However, the effect 
of increasing the quantity of that com- 
pound on the degree of fusion does 
not continue indefinitely. For exam- 
ple, consider a mixture at point R, 
Fig. 7, which is in the region in which 
the potential C 3 A governs the percent- 
age of liquid E. The dotted line RT is 
in a direction directly toward the C 3 A 
point, and represents increasing poten- 
tial C 3 A. When the potential C 3 A is 
increased to a point beyond S, such 
as T, the mixture is no longer in the 
region in which the potential C 3 A 
governs the percentage of liquid. Point 
T is in the region in which the poten- 
tial C 2 S governs the percentage of 
liquid. The quantity of liquid is low- 
ered in passing from S to T, but can 
be increased by increasing the poten- 
tial C 2 S. In considering fusion at 


1455 deg. when the liquid phase is at 
E, C 3 A is the flux in one region and 
C 2 S in the other. Similarly, in the qua- 
ternary system, C 2 S, C3A or C4AF 
may be regarded as a flux in the proc- 
ess of fusion at 1338 deg. when the 
liquid phase is at TV Each of these 
compounds has a particular field of 
influence on the degree of fusion. The 
compound C 3 S is ignored here because 
the potential C 3 S at invariant point T 2 
is so small that it is uncertain whether 
the point is eutectic or peritectic. In 
either case, it is negligible in dealing 
with portland cement compositions. 

As in the ternary system, the quan- 
tity of liquid is proportional to the 
potential C 2 S in low C 2 S compositions 
at the temperature of liquid forma- 
tion. This is in line with experience in 
the commercial process, that low C-S 
compositions are difficult materials to 

Changes in composition may play 
a part in the sloughing off of clinker 
coating or the development of rings 
in the hot zone of the kiln. The line 
R,T, in Fig. 7 has been introduced to 
illustrate the condition. The line is 
drawn at an angle of 60 deg. with the 
base CaO-C 3 A, so that all composi- 
tions on the line are identical in CaO 
content. The Si0 2 /Al 2 3 ratio increas- 
es in passing from Ti to R lB The 
liquid content increases in passing 
from R L to S, and then decreases in 
passing on to T x . Let us suppose that 
composition Ri is maintained in the 
kiln, and that a coating of that com- 
position has been built up. If the 
SiOs/AlaOn ratio in the clay or shale 
drops, so that the clinker has the com- 
position Ti, there is opportunity for 
development of a greater liquid con- 
tent, such as S, at the contact between 
clinker and coating. This may lead to 
sloughing off clinker coating in some 
instances, or building up clinker coat- 
ing in others, depending upon the 
general level of compositions main- 
tained. The effect of an abrupt change 
in SiOs/AUOg ratio is the same wheth- 
er the ratio increases or decreases. The 
possibility of its occurrence depends 
upon the basis for composition con- 

trol. For example, with a constant 
CaO content, as on the line R1T1, 
a change in SiO a /AU0 3 ratio may 
cause the liquid content to rise to a 
maximum, as at S, and then to fall. 
With a constant potential C 2 S the 
liquid content may rise to a maximum 
as the Si0 2 /Al 8 3 ratio decreases, and 
the liquid content then remains con- 
stant, not falling, with further de- 
crease in the ratio. The choice of basis 
for composition control may be im- 
portant in avoiding some abnormalities 
in retention of clinker coating. 

Equilibria above the Temperature 
of Liquid Formation 

So far we have considered equilib- 
ria at the temperature of liquid forma- 
tion, which is 1455 deg. in the ternary 
system C 3 S-C 2 S-C 3 A, and 1338 deg. 
in the quaternary system C3S-C2S- 
C3A-C4AF. Higher temperatures may 
be employed to increase the quantity 
of liquid, to accelerate the chemical 
reactions involved in the production 
of portland cement clinker. States of 
equilibrium in the ternary system at 
higher temperatures will now be con- 

It has been shown in the study of 
Fig. 7 that at maximum heat content 
at 1455 deg. the phases in mixtures 
in triangles C 3 S-C 2 S-E and C 3 S-C 3 A-E 
are those indicated at the vertices. 
With further heating the temperature 
rises, and the liquid follows a boundary 
curve. It should be noted that E (Fig. 
4) is at the intersection of three 
boundary curves, and can be consid- 
ered as being on each one of the three 
curves. The solid phases present when 
the heat content is at a maximum at 
1455 deg. indicates the boundary curve 
which will be followed when the tem- 
perature is raised. For example, a 
mixture in the triangle C 3 S-C 2 S-X con- 
sists of solid phases C : ,S, C 2 S and liq- 
uid E at 1455 dee. maximum heat 
content. As the temperature is raised, 
the liquid follows the boundary be- 
tween the C :1 S and C 2 S primary phase 
regions, starting at E (Fig. 4). Simi- 
larly, when the temperature of a mix- 
ture in the triangle C 3 S-C 3 A-X is 

Fig. 8 : Percent liq- 
uid at 1470 deg. 
min. heat con- 

ed abo\e 1455 dez. the liquid 

- Lindar be een the C 3 S 
d C A pri arj ; reg c 

R. ng 3 Fig. -. it is ^een that 
the be bet n the C 3 S and C-S 

prima: " . regions pas from E 

le C - point 

P. : W in I " I this boun^ 
near the 160 a therm \s mix- 
tun the C vC -X are 
h, abort 1600 deg ;he liquid 
it p il W, I ines ;re drawn 
d W I . C v I C^S pom 
t ~m CHild be tre 
e^ □ the . manner th ;le 

lie Fhe q -^nt pr^ 

tic " ential C A. as ±\ 
the proportional 
The _ d hing in 
: to te that und. rab! 

c will be er red throuL 

:empe: re to ir. - . the 

In the ; mixtures in the tri- 

ie ( •(_ V\. Fig "the liquid 

foil k undary between the C*S 

nary phase re. ons. start - 

lg E. when the temperature rise 

be 5 1455 deg Referring to Fig -, 

it i : t this boundary hort. 

and that t 1470 deg. another invari- 

nt point. D. is encountered. At th, 

point CaO. C > and C A ma exist in 

quihbrium with the liquid. The rela- 

tion between c nposition and percent 
liquid when the liquid arrives at D 
minimum heat content at 1470 deg.) 
is shown in Fig. S. The triang 
C 3 S-0*A-D is narrower than triangle 
C v -C 2 A-E. Fig. 7, but i similar in 
the fact thai the potential QS go\erns 
the quantit f liquid. A different situa- 
tion appears when the heat content at 
l-~0 d :s a maximum. 

Liquid D is capable of existing in 
equilibrium with id CaO. C*S and 
C 3 A. There are four combinations of 
these phases in groups of three, as 

1. C 3 S-C,A-Iiquid D 

I CaO-C 3 S-C A 

3. CaO-C 3 S-liquid D 

4 I O-C A-liquid D 

C nbination 1 h just been conside 

and refer :o minimum fa t con- 
tent at 1- deg Combination 2 Iso 
refers to minimum heat content, but 
onlv for mixtur in the svstem 
CaO-C C 3 A. which cr -tallize com- 
pletely at 1470 d . Combinations 3 
and - refer to maximum heat content. 
This ma> be seen by c mining Fig. . : 
It m be seen from the fact that, 
•arting t D on the boundary between 
the CaO and C^S primary phase re- 
gions or on the boundar between the 
CaO and C*A >ns. the tempera- 

ture r 



Fig. 9 : Percent liq- 
uid and free CaO 

ot 1 470 deg. (max, 
heot content) 

Combinations 3 and 4 are repre- 
sented by the corresponding triangles 
in Fig. 9. Triangle CaO-C :j A-D will 
not be discussed, since the portion of 
the system C 3 S-C 2 S-C :i A which it in- 
cludes is of no interest in relation to 
Portland cement. The triangle CaO- 
QjS-D includes considerable area in 
addition to that in the system C : ,S-C 2 S- 
C 3 A. Since the portion in that system 
is of particular interest, the lines re- 
ferring to percentages of liquid D and 
free CaO are solid lines in the triangle 
C3S-C2S-C3A, and broken lines outside 
of that triangle. 

In Fig. 9, lines are drawn parallel 
to the side CaO-C 3 S to indicate 10 
percent intervals in percentage of liq- 
uid D. Since potential percentages of 
C 3 A may also be represented by lines 
parallel to the same line, as in Fig. 5, 
the quantity of liquid is proportional 
to the potential C 3 A. This is a decided 
change from the conditions at mini- 
mum heat content at the same temper- 
ature. The quadrilateral C3S-X1-Y-Z, 
Fig. 9 (maximum heat content) is a 
part of the triangle C 3 S-C 3 A-Xi. in Fig. 
8 (minimum heat content), in which 
the quantity of liquid is proportional 
to the potential C 2 S. 

It was shown in our study of Fig* 7 
that for ternary cement mixtures of 
low potential C 2 S, at the lowest clink- 
ering temperature, 1455 deg., the per- 
cent of liquid is proportional to the 

potential C 2 S. This is shown by the 
closely spaced lines in that figure. The 
small increase of 1.2 percent in the 
proportion of limestone in passing 
from F to G is accompanied by a de- 
crease in liquid content about 20 per- 
cent to zero. Close control of propor- 
tions of raw materials would be re- 
quired to secure an adequate degree 
of fusion at this low clinkering tem- 
perature. Since high potential C 3 S and 
a corresponding low potential C 2 S 
are sought in the manufacture of high- 
early-strength cement, it is of interest 
to consider the effect of raising the 
temperature of burning. As the tem- 
perature of low C 2 S ternary mixtures 
is raised from 1455 deg. to 1470 deg.. 
the liquid passes from E to D, Fig. 
4. When the liquid arrives at D. 
the percent of liquid is still propor- 
tional to the potential C 2 S, as shown 
in Fig. 8. However, the lines rep- 
resenting percent liquid are more 
closely spaced than in Fig. 7, so that 
for any given composition in the low 
C 2 S range the percent liquid is about 
1.3 times as great as at 1455 deg. With 
further application of heat, there is a 
substantial increase in percent of liq- 
uid without change of temperature, as 
shown in Fig. 9. However, the advan- 
tage of a higher liquid content is offset 
by the fact that free CaO is present as 
an equilibrium phase. The percentages 
of free CaO are represented in Fig. 9 


by lines parallel with the C :I S-D line. 
Since free CaO is an equilibrium 
phase in that region, it will remain 
present as long as the temperature is 
maintained at 1470 deg. and if no 
heat is withdrawn. It may be noted 
that the CaO-C 3 S boundary in Fig. 4 
from point D to the intersection with 
the 1700 deg. isotherm is nearly 
straight and practically coincident with 
a straight line from the QjS point 
to D. The percent of free CaO pres- 
ent as an equilibrium phase in low 
C-S compositions, therefore does not 
change to any great extent when the 
temperature is raised from 1470 deg. 
to 1700 deg. The free CaO present at 
equilibrium at or above 1470 deg. will 
disappear onl\ as the temperature is 
reduced below 1470 deg., but with 
practical rates of cooling such as 
WO! I be possible in a rotary kiln the 
reduction of free CaO content is like- 

1\ to be negligible. The best way of 
avoiding this situation is to maintain 
omf iitions on the low CaO side of 
the ( S-I) line. Ternary compositions 
on the high CaO side mav be burned 
to a low free CaO content b\ main- 
taining temperatures between 1455 
d nd slight!) below 1470 deg. for 

sufficient period ol time. 

In the ternary system CaO -A 1*0 

SiO the CaO primary phase region 
extends outside of the triangle CaO- 
C S-C,A and is partly in the triangle 
C ,v( A-( V It is this condition 
which makes it possible for tree CaO 
to he an equilibrium phase in ternar\ 
Portland cement mixtures under some 
condit as has been described. A 

similar situation exists in the case of 

the quaternary system CaO-AI*0 

SiO*-l .(J.,, as reported by Lea and 
Parker H in which the CaO primary 
ph - volume extends outside of the 

tetrahedron CaO-C J S-C :i A-C,AF. A 

similar situation appears in Swayze 
report ol the s\stem Ca0-Al*0 3 -Si0 
Fe 2 3 as modified by magnesia, in 
which the CaO primary phase volume 
extends outside of the tetrahedron 
CaO~C S-dA-CsA*F. It consequent 
-ppears that the presence of free CaO 
as an equilibrium phase may be expect- 

ed when burning commercial portland 
cement raw mixtures of low potential 
C 2 S content, as has been found in the 
ternary system CaO-Al 2 0^-Si0 3 . 

It has been shown in the discussion 
of Fig. 5 that the line CS-CA is 
the theoretical lime limit. All com- 
positions between that line and the 
CaO vertex contain CaO in excess of 
the amount necessary to form C :i $ 
and C,A. This places a limit upon the 
amount of CaO which can be present 
in a ternary cement mixture. From the 
foregoing study of the presence of 
free CaO as an equilibrium phase in 
low C 2 S mixtures, when burned at 
high temperatures, it may be seen that 
there is another kind of lime limit, 
representing a lime content which 
should not be exceeded if free CaO 

s an equilibrium phase is to be avoid- 

An investigation by Spohn 11 had for 
its purpose the establishment of the 

lime limit" of portland cement. The 
compositions of mixtures at the lime 
limit found by Spohn were located on 
the line C : ,S-D. This lime limit was 
termed ihe "technical lime limit" by 
Spohn. to distinguish it from the theo- 
retical lime limit, which is the line 

( S-C A. The equation of the line is: 

CaO=2.80SiO,+ 1.18 A1,0 3 (18) 

Lea and Parker 8 have examined 
their data on the quaternary system 
CaO-AUO H -Si0 2 -Fe 2 0;, with reference 
to a technical lime limit in that system 
on a basis similar to SpohrTs technical 
lime limit. Their solution of the prob- 
lem, which is in harmony with Spohn's 
remarks on the quaternary system, 
is that the lime limit in the quaternary 
system is represented by a plane pa 
ing through the C 5 S and dAF points 
and through point D. The equation of 
the plane is; 

C r-2.80 Si0 2 - 1.18 AbCM-0.65 FezOa (19) 

Since minor constituents of portland 
cement are not represented in the 
equation, it can only represent ap- 
proximately the technical lime limit 
in commercial portland cement clink- 

Lea and Parker define the lime 
saturation factor' of a cement clink 


er as the ratio of the actual CaO con- 
tent to the technical lime limit, as 
found by substitution in equation 19. 
The saturation factor of a cement 
may be found similarly, if the CaO 
derived from gypsum, that is, 0.70 
times the percent S0 3 , is deducted 
I mm the total CaO. Instead of this 
ratio, we prefer to calculate the "lime 
deficiency/' which is the amount by 
which the CaO content falls short oi 
the technical lime limit. This mav be 

found by substitution in the following 
equation, obtained h\ transposing 
terms in equation 19, as follows: 

L.D.=2.80 Si(). LIS Al.o l 0.65 

I e 3 3 ( aO (20) 

m which I I), represents the lime de 

licicncv , 


Since the plane represented b) equa- 
tion \ { ) passes through the ( |S ami 

( ,A1 points m the spice model, an 
equation in terms oi potential compo- 
sition will not involve these com- 
pounds. 1 he equation corresponding 
to equation 20 is as follows: 

I. .IX 033 ( s 0.18 ( ,\. (21 I 

I'd avoid exceeding the technical lime 

limit, the lime deficiency calculated h\ 

substitution in equation 20 or 21 
should be positive. I he lime deficiency 

to be sought in plant operation will 

depend upon such conditions as fine- 
ness of the raw mix, thoroughness ol 
mixing, and the degree of precision 
in composition control. 

Equations 19-21 are subject to modi- 
fication when required b\ future in- 
vestigations of the quaternary system 
CaO-AlsOa-SiOa-FejOa and of systems 

involving additional components. How- 
ever, they agree quite well with ex- 
perience, and may serve a useful pur- 
pose until more precise relations ar 

This paper has been concerned 
with application of phase equilibrium 
data to the process of burning port- 
land cement clinker. The phase dia- 
gram of the system CaO-AUO O, 

involves only three of the oxides in 
Portland cement. It nevertheless ha^ 
been possible to learn from it some of 
the principles pertaining to the burn- 
ing process, Further investigation of 

the quaternary system CaO-Al 2 3 - 
SiOa-FeaO-! will vield much more in- 
formation. Because of the solid solu- 
tion series C-F-CVWF discovered by 
Swayze 9 some details needed for math- 
ematical treatment of that system 
must be obtained. This introduces dif- 
ficulties in interpretation not found 
in the ternary system. The problems 
concerned with the process of burn- 
ing cement clinker .md with the ^on- 

stitution of portland cement are much 
moi complex than were foreseen 

hen Rankin and \\ ghl invest 
the ternar) stem 

It should be underst* od fi n tl 
foregoing study th it the chan m 
chara md proportions ol ph 

during the burning i s p 

important part in determining 
chai er and p jortions i ph - 
in the < Jed product; ihu is, ii 
cheniK il constil ution oi a c 
clinkei ol an5 n ution 

overned bv the ti tent it und 

oes in the bui ning and cool 
don Reducing conditions o< illv 

exist in a ( ment kiln but it i I I 

ssumed here that the time-tei 

ture curve is the onl\ gO\ n 

tor. At clinkering U be 

clinkei is partiall) fi t; tl it 

com. tins liquid, It is some ht 

that combination ol the 
compounds o ii rs al this si md 

that ill th n is necessar) to seci 
complete combination" is to j 
rin a sufficient!) high I mpt re 
[or a sufficiently long time. Thi> is 
misconception. Ii a given clmkering 
temperature is maintained until 
of equilibrium exists, one or DOOR ce- 
ment compounds will be absent a 

a liquid uill be present There ni 

be a tendency to assum i th ib- 

sent compounds a\c in the liquid but 

this assumption is not sound. Th 

atomic arrangement in the liquid 

haphazard. SO that the liquid can n* 
be re rded as being composed the 
cement compounds n. In a paper 

on the constitution of glass, Morey 11 

ipres! the situation as follows: 
The existence of certain compounds 

s the stable products of er\ Jliza- 


tion of a liquid is no evidence that 
they exist as such in the liquid, and 
no knowledge we have at present per- 
mits the identification of anv com- 
pounds existing in the liquid state." 

Following the burning operation, 
the clinker may be cooled so rapidly 
that crystallization cannot occur. The 
liquid then hardens to a glass. The 
glass, like the liquid, is not composed 
of cement compounds. The only 
sound reason for estimating the po- 
tential compound composition of glass 
in clinker is to determine the approxi- 
mate quantity of each compound which 
is not present as a result of failure 
of the liquid to crystallize. The quan- 
tities of the compounds actually pres- 
ent ma\ then be found bv difference. 
It should be clear that the cooling 
operation pla\s an important part in 
fixing the chemical constitution of ce- 
ment clinker. In fact, if a mixture of 
any given composition is maintained 
at Jinkering temperature until equi- 
librium is attained, the subsequent 
c linn operation governs the chemi- 
cal constitution oi the finished prod- 

It has been the purpose of this pa- 
per to use the phase diagram of the 
tcrnan system CaO-AKO -SiO-* as a 
for demonstrating the manner 
in which a ph : diagram ma\ be ap- 
plied in dealing with problems per- 
taining to the manufacture of port- 
land anient, and to a stud} of the 

1 constitution of the product. 
Chemists in direct contact with the 
mai ture of cement will find it 

helpful U :ome familiar with the 



me of the principles pertaining to 
the interpretation of phase diagrams 
ha\e been applied to the phase dia- 
gram of the system CaO-Al 2 3 -Si0 2 , 
with the purpose of gaining an under- 
standing of the clinkerin_ operation. 
It has been found that: 

1. In the process of fusion. liquid 
is formed at the expense of the solid 
phases present. The process may con- 
tinue until one of the solid phases dis- 

appears. The percentage of that phase 
in the potential composition of the 
mixture governs the percent of liquid. 

2. As the proportion of limestone 
in the raw mix is increased, a point is 
reached at which C 2 S becomes the 
disappearing phase. The effect of in- 
creasing lime content in lowering the 
percent of liquid becomes very large, 
so that burning becomes increasingly 


3. The "technical lime limit" is the 
maximum CaO content which may be 
maintained without encountering free 
CaO as an equilibrium phase. This 
technical, or practical, lime limit is 
expressed by the equation, 

CaO = 2.80 SiO* + 1.18 AM>a + 0.65 FesOs 

4. When the technical lime limit is 
exceeded, the free lime present as an 
equilibrium phase is not removed by 
prolonged burning, or by increasing 
the temperature, but can disappear 
only bv extremelv slow cooling. 

5. The ideal state represented by 
the potential compound composition 
is attained only as a result of extreme- 
ly slow cooling. If equilibrium is at- 
tained at a high temperature, the cool- 
ing operation determines the chemical 
nature of the product. 

Study of the phase diagram involv- 
ing onh the three major components 
of portland cement has brought out 
ome principles which are helpful in 
understanding the chemistry of the 
burning operation. Further investiga- 
tions of systems involving the minor 
components may be expected to yield 
more precise knowledge of what goes 
on in the kiln. 

(1) <*. A. Rankin and F. E. Wright, Am. J. 

ScL. | 4 1 39 t 1-79 (1915 k 
(2j L. A. Dahl, Rock Product* 

<19. - . 

N. L. Bo wen and J. W. Greig, J. Am. 

Ceram. Soc, 7 4 1. . — 1924). 
(4 J IV. 'Jreig. Am. J. ScL, (£ !:, -41 

I 1927 . 

W. Eitel and W. Bussem. Zeit. Kristal- 

lographie, ' 

(6; B. 1 i La Chimica e l'Indu>iria, 1. 

461 IT 
(7; F. M. Lea and T. W. ParV Phil. Trans. 

Royal Soc., 234, 731. 1 (T 

F. M. Lea and T. W, Parker, Bid*. Re*. 

Tech. Paper No. 16 U935 I 

M. A. Swayze. Am. J. ScL, 244, 1; C 


. C. Hansen. L. T. Brownmiller and R. 

H. Bogne. J. Am. Chem. Soc.. 396 

(191 . 
(U) Eberhard Spohn, Zement, 21, 702 (1932). 
- Geonre W. Morey, J. Am. Ceram. Soc., 

I 15-28 (1934 . 

Hr ll< tin- Published h ii.. 

Research Department 

\ii ■•* arch and Development Division 

of the 

1'orllaml ( !rtii<-nl \ notation 

illetin I 

"fc ition of J t Cli 

SiO j-AI ,0, 4CaO«Al O.-l r 0, 

\>< itures," lr. I \ I 

i i 


1 1 

I i0 

ng Ten 

•illetin 2 

I he i ill 

us a Sj il Cas< 

I i \ I J • I nl 




. mII n '. 

kai >l dm i I Nnnl! 

I>hci ei II Bu uom ol ' 

■ hi - nt ( ited I- n | ilattd upt 






| ( . tm 4— F iii ill. i itud . o h« J' 

1 1 


\ Woi h 

i on 

H ^rhi-siH tor I 

CS c 


1 1 


ullctin 5A 

it to HulU-tin 5 I 
F u i 


II \\ I 


A .v ki 

r mA ¥ 

t i 

Bull n 

Dyn Tes i* 

1 1 


K ; i iti ms for iputin* I 

sio I Resonant Freque ics 


i • 

Bull n 

Flexural Vihr n ot I ni titled I < [ 


i. . 

BulL - n 

Should Portlan emen' B spcrsei 


Bull n 10 — "Interpr Phase I Ternar 

Bulletin 11 

Bulletin 12 

Bulletin 13 

"Shrinkage Stresses in Concrete: Part 1 — Shrinkage (or Swelling), 
Its Effect upon Displacements and Stresses in Slabs and Beams of 
Homogeneous. Isothopic, Elastic Material; Part 2— Application of the 
Theory Presented in Part 1 to Experimental Results"; by Gerald 
Pickett, March, 1946. 

Reprinted from Journal of the American Concrete Institute (January and February, 
1' I; Proceed l . 42. lo3. 361 (\9ib). 

''The Influence of Gypsum on the Hydration and Properties of Port- 
land Cement Pastes," by William Lerch, March, 1946. 

Reprinted from Proceeding imerican Society for Testing Materials, 46, 1251 (19 . 

"Tests of Concretes Containing Air-Entraining Portland Cements or 
Air-Entraining Materials Added to Batch at Mixer," by H. F. Goxxer- 
MAN, April, 1947. 

R. -printed from Journal of the American Concrete Institute (June. 191H; Proceedings. 

Ki. i" (1944); •■ supplemental^ data and anal - s, reprinted from Supplement 

iNovi r. 1914 i : Proceedings, 40. ">U8-1 <1914i. 

Bulletin 14 — "An Explanation of the Titration Values Obtained 

Sugar-Solubiiity Test for Portland Cement," by 

March. 1947. 

Reprinted from ASTM H . No. 145, 62 (March, 1947). 

in the Merriman 
William Lerch, 

Bulletin 15 

Bulletin 1 

Bulletin 1" 

"The Camera Lucida Method for Measuring Air Voids in Hardened 
Concrete." by George J. Verbeck, May, 1947. 

R from . -nal of the American ( e Institute (May, 19*7); Proceedings, 

43, . . 1947). 

"Development and Study of Apparatus and Methods for the Determina- 
. tion of the Air Content of Fresh Concrete," by Carl A. Menzel, Ma; 

• 47. 

R • i., Journal of the tmerb Con I tuu (May, 1" 7); Proceeding 

1 !. i ■ 

"The Problem of Proportioning Portland Cement Raw Mixtures: Part 
I— A General View of the Problem; Part II — Mathematical Study of 
the Problem; Part III — Application to Typical Processes; Part IV-— 
Direct Control of Potential Composition"; by L. A. Dahi.. June. 1947. 

Reprint! b i Rock P SO, No. I, 109; V 107; V ;. 92; No. 1. 122 L947). 

Bulletin 18 — "The System CaO-SiCL-H.O and the Hydration of the Calcium Sili- 
cates," by Ha ld H. Sti ixoi'R. June. 1947. 

Reprinted i H- . 40. H91 ()91T>. 

"Procedures for Determining the Air Content of Freshly-Mixed Con- 
crete by the Rolling and Pressure Methods," by Carl A. Menzel, 
Tui 1947. 

Reprinted I Pro imet m S Testing Maten 17. 833 11917 

"The Effect of Change in Moisture-Content on the Creep of Concrete 
under a Sustained Load," by Gerald Pickett, July, 1947. 

]; inted Erom Journal of the Am Concrete Institute (February, 1942); Proceed- 

es. AH. 333 (1942). 

Bulletin 19 

Bulletin 20 

Bulletin 21 


Bulletin 22 

Bulletin 23 

Bulletin 24 

Effect of Gypsum Content and Other Factors on Shrinkage of Con- 
crete Prisms," by Gerald Pickett, October, 1947. 

R .] j >umal o\ thi i n Coi Institute tober, 1947); I' 

4 4. 149 (19 

" Studies of the Physical Properties of Hardened Portland Cement 
Paste,'* by T. C Power- and T. L. Brown yard, March, 1948. 

Reprinl Erom Jour t Ou inn in Com ret* I litut (October-D« 

January-April, 194" Pn dm. 13. 101. 249, W9« >19, 669. 845, 933 (1947), 

'Effect of Carbon Black and Black Iron Oxide on Air Content and 
Durability of Concrete," by Ti *as G. Taylor, May, 1948. 

R rinted fr-rn Journal of : an Concrete Institute (April, 19 i Proceeding 

44. 613 (19 

•"Effect of Entrained Air on Concretes Made with So-Called l Sand- 
GraveP Aggregates/* by Paul Klieger, November, 1948. 

Reprinted Erom Journal oj the An an Concrete institute (( ; Proceed- 

ings 4". 149 1 1949K 


Bulletin 25 


"A Discussion of Cement Hydration in Relation to the Curing of Con 
crete/' by T. C. Powers, August, 1948. 

Reprinted from Prat dingi oj the Highway Research Board, 27. 178 (1947). 

Bulletin 26 — "Long-Time Study of Cement Performance in Concrete." This bulletin 

comprises tour installments of the report of this investigation, by F. R. 
McMillan, 1. L. Tyler, W. C. Hansen, William Lerch, C. L Ford, 
and L. S. Brow x, August, 1948. 

lU'i'i inh-.l from Journal of the imei m Concrete Institute (February-Ma) 1948); 
Proceeding 14, 111 553, 743, 877 (1948). 

Bulletin 27 

Bulletin 28 

Bulletin 29 

Bulletin 30 

Bulletin 31 

Bulletin 32 

Bulletin 33 

Bulletin 34 

Bulletin 35 

Bulletin 36 

Bulletin 37 

Bulletin 38 

Bulletin 39 

"Determination of the Air Content of Mortars by the Pressure Meth- 
od/' by Thomas G. Taylor, February, 1949. 

Reprinted from ASTM Bullet No. 155, \\ December, 1948). 

"A Polarographic Method for the Direct Determination of Aluminum 
Oxide in Portland Cement/' by C L. Ford and Lorrayne Le Mar, 
April 1949. 

Reprintnl from ISTM Bulletin, No. 157. 66 (March, 1949). 

"The Nonevaporable Water Content of Hardened Portland-Cement 
Paste — Its Significance for Concrete Research and Its Methods of 
Determination," by T. C. Powers, June, 1949. 

Reprinted from iSTM Bulletin, No. 158, 68 (May, 1949). 

"Long-Time Study of Cement Performance in Concrete — Chapter 5, 
Concrete Exposed to Sulfate Soils," by F. R. M< Mn « sr, T. E. Stan- 
ton, I. L. Tyler and W. C. Hansen, December, 1949. 

Reprinted from a Special Publication of the American Concrete Institute (1919). 

"Studies of Some Methods of Avoiding the Expansion and Pattern 
Cracking Associated with the Alkali-Aggregate Reaction," by Wil- 
liam Lerch, February, 1950. 

Reprinted fr<»m $pe< l> knical Publication No. 99* published b) American Socictj 

for Testing Materials (1950). 

^Long-Time Study of Cement Performance in Concrete — Chapter 6. 
The Heats of Hydration of the Cements," by George J. Verbei k and 
Cecil W. Foster, October, 1949. 

i;, ;.,,,,!. -,] from Port tmerit in Sc • foi I tg M erials, 50, L235 (1950). 

"The Air Requirements of Frost-Resistant Concrete," by T. C. Powers ; 
discus > ion by T. F. Willis. 

Reprinted from Proceeding* of the Highu ' h Board. 29, 184 (1949). 

"Aqueous Cementitious Systems Containing Lime and Alumina," by 
Harold H. Steinour, February, 1951. 

"Linear Traverse Technique for Measurement of Air in Hardened 
Concrete/ 1 by L. S. Brown and C. U. Pierson, February, 1951. 

\\ .rnih-.! from Journal oj the imerican Cot e Institute (October, L950) ; Proceed- . 
ings, IT. 117 (1951). 

-"Soniscope Tests Concrete Structures/' by E. A. Whitehurst, February, 

Reprinted from Journal oj the (men Con ete Institute (February, 1951); Pro d- 

ings, 17, 133 U951 I. 


Dilatometer Method for Determination of Thermal Coefficient of Ex- 
pansion of Fine and Coarse Aggregate," by George J. Verbeck and 
Werner K. Has-, September, 1951. 

(•printed from Proceedings of Highway Research Board, 30, 187 (1951). 

"Long-Time Study of Cement Performance in Concrete — Chapter 7. 
New York Test Road," by F. H. Jackson and T. L. Tyler, October, 1951. 

Reprinted from Journal of the imerican Concrete Institute ijun.-, 1951); Pro< 
47, 773 I 1951 K 

"Changes in Characteristics of Portland Cement as Exhibited by Labo- 
ratory Tests Over the Period 1904 to 1950," by H. F. Gonnerman and 

William Lerch. 

Reprinted from Special Publication No. 127, published b) American Societj for Testing 



Bulletin 40 — ''Studies of the Effect of Entrained Air on the Strength and Durability 

of Concretes Made with Various Maximum Sizes of Aggregate/' by 
Paul Klieger. 

I -inted from P t •■ H.^hwva* r\ h Board, 31. 1"" 19". 

Bulletin 41 — "Effect of Settlement of Concrete on Results of Pull-Out Bond Tests," 

By Car: A. Mexzel. November, 1952. 

Bulletin 42 — " An Investigation of Bond Anchorage and Related Factors in Rein- 
forced Concrete Beams," by Carl A. Mexzel and William M. Wooi - 
Noveml . 1952. 

Bulletin 43 — "Ten Year Report on the Long-Time Study of Cement Performance 

in Concrete," by Advis ry Commil e of the Long-Time Study of Cement 
I 'finance in Concrete. R. F. Blaxk>. Chairman. 

Reprintec urnmi of the Amer i Con< tut larch. 19 r : Proceeding 

4M, rK»l " I. 

Bulletin 44 — "The Reactions and Thermochemistry of Cement Hydration at Ordi- 
nary Temperature/' bj Harold H. Stei] vr. 

Reprinted from Thir uionml 5 mposium on thr ( - -neat. London. 

Sept. 19". 

Bulletin 45 — "Investigations of the Hydration Expansion Characteristics of Portland 

Cement." y H. F Gonnerman, Wm. Lerch. and Thomas M. White- 
sir Ju I : 

Bulletin 46 — "Theory of Volume Changes in Hardened Portland Cement Paste 

During Freezing/' T. C Powers and R. A. Helmuth. 

Reprinted from P' lings of the Hifhu ': vrck Bomi 32. _&5 (195 

Bulletin 4" — "The Determination of Non-Evaporable Water in Hardened Portland 

Cement Paste," L. E. Cop- <d and Jc N C Have-. 

Reprinted from - f Bullet: No. 194. mber. 1952 

Bulletin 48 — 'The Heats of Hydration of Tricalcium Silicate and beta-Dicalcium 

Silicate." \ Stephen Brunaur, J. C. Haves and W. E. Ha — 

Reprinted d > 58, 279 

Bulletin 49 — "Void Spacing as a Basis for Producing Air-Entrained Concrete." by 


Reprinte . nM of imericam C*. ele Ims Ma\. 1954); Proceedings, 

r,i>. 741 

Bulletin 49A — Discussion of the paper "Void Spacing as a Basis for Producing Air- 
Entrained Concrete," by J. E. Backstrom, R. \Y. Burrows, V. E. 
Wolkodoff and Author, t. C Powers. 

Reprinted he A merit. Concrete Institute « Dec., Par -. 19"4 < : Pro- 

Bulletin 50 — "The Hydrates of Magnesium Perchlorate." by L. E. Copelaxd and R. 

H. Bragg. 

Rer :. Tkt iaiI oj P - 58. 1075 « 1954 » . 

Bulletin 51 — "Determination of Sodium and Potassium Oxides in Portland Cement 

Raw Materials and Mixtures, and Similar Silicates by Flame Photom- 
etry/ 1 Ford. 

Reprinted from Analytical Chemistr . 4*>. 1578 i 1954 1. 

Bulletin 52— "Self Desiccation in Portland Cement Pastes." by L. E. Copelakd and 

R. H. Bragg. 

Reprinted from ASTM Bulb So. 204. 34 »Fbruar " . 

Bulletin 53 — Permeability of Portland Cement Pastes/' bv T. C Powers, L. E. 

( pel and, J. C. Hayes and H. M. Manx. 

Reprinted from J .. ike Am i Concrete Jr. 195 Pr ;. 

. 51, 285, 1955 • . 

Bulletin 54 — "Some Observations on the Mechanics of Alkali-Aggregate Reaction, 

by L. S. Brown. 

Reprinted from ASTM Bulletin. No. 2»>~. April. 195" 



Bulletin 55 — "An Interpretation of Published Researches on the Alkali-Aggregate 

Reaction: Part 1 — The Chemical Reactions and Mechanism of Expan- 
sion; Part 2 — A Hypothesis Concerning Safe and Unsafe Reactions 
with Reactive Silica in Concrete," by T. C. Powers and H, H. Steinour. 

Reprinted From Journal of the American Concrete Institute (February and April, 1955 I 
Proceedings, 51, pp. t97 and 785 (1955). 

Bulletin 56 — "Comparison of Results of Three Methods for Determining Young's 

Modulus of Elasticity of Concrete," by R. E. Philleo. 

Reprinted from Jour/ml of the American ( urn rrte Institute I Limiury, 1955) ; Proceed 
ings, 51, 4ol ( 1955). 

Bulletin 57 


Osmotic Studies and Hypothesis Concerning Alkali-Aggregate Re- 
action," by George J. Verbeck and Charles Gramlich. 

Reprinted from Proceedings, tmerican Society for Testing Materials, Vol. 55, p. — , 

Bulletin 58 — "Basic Considerations Pertaining to Freezing and Thawing Tests," by 

T. C. Powers. 

Reprinted from Proceedings, American Society for Testing Materials, Vol. 55, p. — , 

Bulletin 59 — "New Study on Reactions in Burning Cement Raw Materials," by 

L. A. Dahl. 

Reprinted from Rock Products, 58, No. 5, 71; No. 6, 102; No. 7, 78 (1955).